Not a chance matey. (Legally). However...and I’m not advocating illegality, others have done very very short flights, ‘cut n run’ then edited the flights into a short film, (see you tube). But be aware, that any flying around London will most likely be illegal and attract the attention of the authorities, particularly in these terror obsessed times. London city airport is nearby, as is the headquarters of MIi5, not to mention all the landmarks of one of the most famous capital cities in the world.
My advice...just forget the drone, take your camera and have a great time, it’s not worth getting into big trouble over just for a few shots with a drone.